In this paper we consider the effect of boundary damping on a cantilevered Timoshenko beam with a rigid body attached to the free end. We establish the efficiency and accuracy of the finite element method for calculating the eigenvalues and eigenmodes. Although no conclusion could be drawn with regard to the stabilization of the system, interesting phenomena concerning the damped vibration spec...

abstract: in this paper, nonlocal euler–bernoulli beam theory is employed for transverse vibration analysis of an initially pre-stressed size-dependent rotating nanotube. the nonlocal eringen theory takes into account the effect of small size, which enables the present model to become effective in the analysis and design of nanosensors and nanoactuators. governing equations are derived through ...

Buckling analysis of a functionally graded (FG) nanobeam resting on two-parameter elastic foundation is presented based on third-order shear deformation beam theory (TOSDBT). The in-plane displacement of TOSDBT has parabolic variation through the beam thickness. Also, TOSDBT accounts for shear deformation effect and verifies stress-free boundary conditions on upper and lower faces of FG nanobea...

The free vibration analysis of rotating functionally graded (FG) nano-beams under an in-plane thermal loading is provided for the first time in this paper. The formulation used is based on Euler-Bernoulli beam theory through Hamilton’s principle and the small scale effect has been formulated using the Eringen elasticity theory. Then, they are solved by a generalized differential quadrature meth...

This work presents a method to find the exact solutions for the free vibration analysis of a delaminated beam based on the Timoshenko type with different boundary conditions. The solutions are obtained by the method of Lagrange multipliers in which the free vibration problem is posed as a constrained variational problem. The Legendre orthogonal polynomials are used as the beam eigenfunctions. N...

Abstract: In the present article, a semi-analytical technique to investigate free bending vibration behavior of axially functionally graded non-prismatic Timoshenko beam subjected to a point force at both ends is developed based on the power series expansions. The beam is assumed to be made of linear elastic and isotropic material with constant Poisson ratio. Material properties including the ...

Based on generalized laminate plate theory, the formulation of a one-dimensional beam finite element with layer-wise constant shear (BLCS) is presented. The linear layer-wise representation of in-plane displacements permit accurate computation of normal stresses and transverse shear stresses on each layer for laminated beams with dissimilar ply stiffnesses. The BLCS formulation is equivalent to...

In this paper, a comprehensive study is presented on the effect of beam's length, shear deformation and beam's theory on the dynamic modeling of single-link flexible manipulator. At the first step, Euler-Bernoulli beams theory (EBBT) is adopted. According to this model the effect of shear deformation is neglected. So, this model is only reliable for the case of slender beam. When the beam is sh...

In this article, the free vibration analysis of magneto-electro-elastic (MEE) Timoshenko micro beam model based on surface stress effect and modified strain gradient theory (MSGT) under moving nano-particle is presented. The governing equations of motion using Hamilton’s principle are derived and these equations are solved using differential quadrature method (DQM). The effects of dimensionless...

Recent results concerning the application of Lie transformation group methods to structural mechanics are presented. Focus is placed on the point Lie symmetries and conservation laws inherent to the Bernoulli–Euler and Timoshenko beam theories as well as to the Marguerrevon Kármán equations describing the large deflection of thin elastic shallow shells within the framework of the nonlinear Donn...